Define 
as the quantity appearing in Waring's problem,
then Euler conjectured that
 |
where 
is the floor function.
Euler's Conjecture
See also
Euler's Graeco-Roman Squares Conjecture, Euler Quartic Conjecture, Euler's Sum of Powers Conjecture, Waring's ProblemExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Euler's Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EulersConjecture.html